I have referenced a plane / surface intersect in the sketcher. It results in a curve.

I draw a line from one end to the other using critical pick.
It selects the end points and the line is created. No visual constraint is displayed.
Toggling constraints and unblank all does not display any constraint markers

Constraint Status all turns green colour.

Next I added a point to curve constraint, it allowed me to do it!. Even though the Constraint Status was green? Both times before and after adding saying All constrained geometry is well defined
I am confused

Mark,
I am not sure why you are allowed to add a 'visible' constraint. There is some mystery in here.
However there are things call 'implied' constraints which you do not see. Point ot point when snap drawn seems to be the common one as per your example.

IMO there needs to be an option to 'show' 'implied' constraints as just occasionally they create a difficulty.

Sometimes I purposely draw the line away from its final home then apply constraints so I know exactly what is going on.
ZW need to respond to your question...
Cheers - Paul